Memoirs of the School of Engineering, Nagoya University Vol.50, No.1/2 (1998) SHAPE OPTIMIZATION OF SHELL AND SPATIAL STRUCTURE FOR SPECIFIED STRESS DISTRIBUTION Hiroshi OHMORI* and Kenji YAMAMOTO  Department of Architecture (Received December 4, 1997)

Abstract
Shells and spatial structures are adopted for construction of large span structures in which a large space is realized without columns as the structural components. In those cases, the structures are expected to resist against various design loads mainly through their extremely strong capability which can be acquired through in-plane or membrane stress resultants and this is just the reason by which they themselves stand for external loads without columns as their structural components in the large span structures. Up to this time, shells and spatial structures have been frequently adopted as a structure which can realize large span constructions, where, however, purely geometrical shapes like spheres, cylinders and their parts have been adopted as their structural forms. It can be said relatively easy to handle purely geometrical shapes from the view-point of both structural analysis and construction design, where, however, we have to handle bending stress resultants which are inevitably accompanied with especially in the vicinity of their supporting boundaries. From the view point as mentioned above about the mechanical characteristics of shell and spatial structure, it would be consistent if we could have those bending stresses rationally treated not through cheap tricks like addition of shell thickness but some essential treatments which are originated from the investigation of the forms themselves of the structures. In the present work, direct treatment method of stress distribution in shells and spatial structures are shown, which enables us to obtain approximately bending free structural forms. Numerical calculation has been carried out for both axisymmetric shells and spatial structures, where effectiveness of this method has been clearly shown and mechanical characteristics of the obtained surface of both shells and spaIn the present work, direct treatment method of stress distribution in shells and spatial structures are shown, which enables us to obtain approximately bending free structural forms. Numerical calculation has been carried out for both axisymmetric shells and spatial structures, where effectiveness of this method has been clearly shown and mechanical characteristics of the obtained surface of both shells and spatial structures are discussed as well. Finally, some feasibility studies adopting RC shells as an example are also shown.

Keywords: shape optimization, sensitivity analysis, shell, space structure, space frame, bending moment, nonlinear programing, sequential programing method

*Department of Architecture, School of Engineering, Nagoya University  Department of Architecture, Faculty of Engineering, Kagoshima University